Einstein-Euler equations for matter spacetimes with Gowdy symmetry

Philippe G. LeFloch[1]

  • [1] Laboratoire Jacques-Louis Lions & Centre National de la Recherche Scientifique Université Pierre et Marie Curie (Paris 6) 4 Place Jussieu 75252 Paris France

Séminaire Équations aux dérivées partielles (2008-2009)

  • Volume: 2008-2009, page 1-15

Abstract

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We investigate the initial value problem for the Einstein-Euler equations of general relativity under the assumption of Gowdy symmetry on T 3 . Given an arbitrary initial data set, we establish the existence of a globally hyperbolic future development and we provide a global foliation of this spacetime in terms of a geometrically defined time-function coinciding with the area of the orbits of the symmetry group. This allows us to construct matter spacetimes with weak regularity which admit, both, impulsive gravitational waves and shock waves. The cosmic censorhip conjecture is established in the polarized case.

How to cite

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LeFloch, Philippe G.. "Einstein-Euler equations for matter spacetimes with Gowdy symmetry." Séminaire Équations aux dérivées partielles 2008-2009 (2008-2009): 1-15. <http://eudml.org/doc/11196>.

@article{LeFloch2008-2009,
abstract = {We investigate the initial value problem for the Einstein-Euler equations of general relativity under the assumption of Gowdy symmetry on $T^3$. Given an arbitrary initial data set, we establish the existence of a globally hyperbolic future development and we provide a global foliation of this spacetime in terms of a geometrically defined time-function coinciding with the area of the orbits of the symmetry group. This allows us to construct matter spacetimes with weak regularity which admit, both, impulsive gravitational waves and shock waves. The cosmic censorhip conjecture is established in the polarized case.},
affiliation = {Laboratoire Jacques-Louis Lions & Centre National de la Recherche Scientifique Université Pierre et Marie Curie (Paris 6) 4 Place Jussieu 75252 Paris France},
author = {LeFloch, Philippe G.},
journal = {Séminaire Équations aux dérivées partielles},
keywords = {general relativity; Gowdy symmetry; Einstein-Euler equations; perfect fluid; impulsive gravitational wave; shock wave},
language = {eng},
pages = {1-15},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Einstein-Euler equations for matter spacetimes with Gowdy symmetry},
url = {http://eudml.org/doc/11196},
volume = {2008-2009},
year = {2008-2009},
}

TY - JOUR
AU - LeFloch, Philippe G.
TI - Einstein-Euler equations for matter spacetimes with Gowdy symmetry
JO - Séminaire Équations aux dérivées partielles
PY - 2008-2009
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 2008-2009
SP - 1
EP - 15
AB - We investigate the initial value problem for the Einstein-Euler equations of general relativity under the assumption of Gowdy symmetry on $T^3$. Given an arbitrary initial data set, we establish the existence of a globally hyperbolic future development and we provide a global foliation of this spacetime in terms of a geometrically defined time-function coinciding with the area of the orbits of the symmetry group. This allows us to construct matter spacetimes with weak regularity which admit, both, impulsive gravitational waves and shock waves. The cosmic censorhip conjecture is established in the polarized case.
LA - eng
KW - general relativity; Gowdy symmetry; Einstein-Euler equations; perfect fluid; impulsive gravitational wave; shock wave
UR - http://eudml.org/doc/11196
ER -

References

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